Geometry, theoretical arithmetic and algebra, these subjects have no other principles except definitions and axioms, and no other proof process except deduction. But in this process, they have integrated simplicity, Complexity, rigor and generality are characteristics not possessed by other disciplines. ---Whewell, W.

Descartes' analytic geometry and Newton's calculus have been expanded to In the bizarre mathematical methods of Lobachevsky, Riemann, Gauss and Salvesto (this expansion is bolder than that of any discipline recorded in the history of philosophy). In fact, mathematics is not only the It is an indispensable tool for all disciplines, and it flies freely without regard to the constraints of intuitive feelings. Historically, mathematics has never shown its supremacy over pure reasoning as it does today. ---ButlerNicholas Murray